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Preface Acknowledgments 9 Invariance Theory 9.1 Review of Affine and Riemannian Geometry. 9.2 Invariance Theory in the Riemannian Setting 9.3 The Chern-Gauss-Bonnet Formula 9.4 Pseudo-Kaihler Manifolds 9.5 VSI Manifolds 9.6 Invariants that are not of Weyl Type 10 Homothety Homogeneity and Local Homogeneity 10.1 Introduction 10.2 Classification Results 10.3 Completeness 10.4 3-dimensional Walker Lorentzian Manifolds I: Curvature Homogeneity. 10.5 Walker Lorentzian Manifolds II: Homothety Curvature Homogeneity 10.6 Stability 10.7 Locally Homogeneous Metric G-structures 11 Ricci Solitons 11.1 Introduction 11.2 Riemanian Homogeneous Ricci Almost Solitons 11.3 Lorentzian Homogeneous Gradient Ricci Solitons 11.4 Riemannian Locally Conformally Flat Gradient Ricci Solitons 11.5 Lorentzian Locally Conformally Flat Gradient Ricci Solitons 11.6 Neutral Signature Self-dual Gradient Ricci Almost Solitons Bibliography Authors'Biographies Index ±à¼­ÊÖ¼Ç